Dynamic polarization potential of 12C+12C system at molecular-resonance energies

The nuclear reaction dynamics leading to the formation of recently discovered resonance in the mutual-0₂ ⁺ channel of the ¹²C+¹²C inelastic scattering around E _c.m.≃ 32 MeV is studied in terms of the dynamic polarization potential (DPP) induced by the channel coupling among various excited states in ¹²C. The microscopic 3α cluster-model wave functions are used to generate the ¹²C−¹²C diagonal and coupling potentials in the double-folding model. It is found that DPP for the 0₂ ⁺+ 0₂ ⁺ channel is an unusually strong attractive potential which even exceeds the zeroth-order folding-model potential of this channel around the nuclear surface region and that the strong coupling between the 0₂ ⁺ and 2₂ ⁺ states is predominantly responsible for the unusual DPP in this channel. The effective potential, the sum of the original folding-model potential and the attractive DPP, is found to generates resonance states in the same energy region as that of the resonance states generated by the original folding-model potential but the former states are found to be higher-nodal states having four additional radial nodes. Similar but more moderate property of DPP is also found in the entrance (elastic) channel. These results suggest that the reaction dynamics of generating the resonance in the ¹²C(0₂ ⁺) +¹²C(0₂ ⁺) channel may rather differ from that of the simple crossing of the zeroth-order molecular band generated by the potentials in the entrance and exit channels suggested by the standard band-crossing model. Received: 17 December 1998 / Revised version: 1 March 1999     

Fusion cross sections for 10,11B+12C at sub-Coulomb energies

Total fusion cross sections for the ¹⁰B + ¹²C and ¹¹B + ¹²C reactions have been determined over a 5 MeV (c.m.) energy range extending to ≈ 3 MeV below the Coulomb barrier. Absolute γ-ray yields for specific transitions in the de-excitation of the heavy products following compound nucleus decay were measured using a Ge(Li) detector. Statistical model calculations of the decay modes of the compound nucleus have been used to deduce, from the γ-ray data, cross sections for single proton, neutron and α-particle emission, and to determine total cross sections for compound nucleus formation. No evidence has been found for sub-Coulomb resonances in either reaction. The total reaction cross sections are compared with optical model calculations using different parameter sets and the observed trend in the very low energy cross sections is discussed relative to other reactions in the same mass region.     

Measurement of the antiproton-nucleus annihilation cross-section at very low energies

The ASACUSA collaboration at the Antiproton Decelerator at CERN is planning to measure the hyperfine splitting of the ground state of antihydrogen using an atomic beam line. This will be a measurement of the antiproton magnetic moment, and also a test of the CPT invariance. The planned experimental method and setup, including the radiofrequency resonance cavity, are described, and results of Monte Carlo simulations are shown. These simulations predict that the antihydrogen ground-state hyperfine splitting can be determined with a relative precision of ～10^???7.     

The12C+12C reaction at subcoulomb energies (I)

The reaction¹²C+¹²C has been studied in the energy rangeE _cm=2.45–6.15 MeV byγ-ray spectroscopy. Gamma-ray transitions from a large number of excited states in²⁰Ne,²³Na and²³Mg were observed, which show strong and rapid yield variations. When the influence of the Coulomb barrier is removed, these structures appear superimposed on a flat reaction yield, which does not show a strong increase at low energies, in contrast to previous work. These results obviate the need for the hypothesis of absorption under the barrier at least down toE _cm=2.45 MeV. The nuclear and astrophysical aspects of the data are discussed.     

The12C+12C reaction at subcoulomb energies (II)

The reaction¹²C+¹²C has been studied in the energy range E_c.m.=2.8–6.3 MeV by charged-particle spectroscopy. Angular distributions of the proton and α-particle exit channels were obtained. The excitation functions do not reveal evidence for the phenomenon of absorption under the barrier. The data have been extrapolated to the energy region of astrophysical interest. The existence of reported and new intermediate resonance structures is discussed.     

Oscillations in the excitation function for complete fusion of 6O+12C at low energies

The excitation function of the complete fusion of ¹⁶O + ¹²C has been measured in the range E_c.m.=8.5?12.9 MeV. It contains oscillations which have already been observed at higher energies. Some of these oscillations are tentatively in terms of a rotational band.     

Global examination of the 12C + 12C reaction data at low and intermediate energies

We examine the ¹²C + ¹²C elastic scattering over a wide energy range from 32.0 to 70.7 MeV in the laboratory system within the framework of the optical model and the coupled-channels formalism. The ¹²C + ¹²C system has been extensively studied within and over this energy range in the past. These efforts have been futile in determining the shape of the nuclear potential in the low energy region and in describing the individual angular distributions, single-angle 50° to 90° excitation functions and reaction cross-section data simultaneously. In order to address these problems systematically, we propose a potential that belongs to a family other than the one used to describe higher energy experimental data and show that it is possible to use it over this wide energy range. This potential also predicts the resonances at correct energies with reasonable widths.     

Cross sections for 6Li production in the reactions 10B + 16O and 12C + 14N at low energies

Absolute cross sections have been measured for the reactions ¹⁰B(¹⁶O, ⁶Li)²⁰Ne and ¹²C(¹⁴N, ⁶Li)²⁰Ne at several energies in the range E_c.m. = 7.5–16.2 MeV, and 13.8–16.6 MeV, respectively. The predictions of Hauser-Feshbach calculations show generally good agreement with the experimental data without parameter variation. The consequences of an angular momentum cutoff in the entrance channel and in the compound nucleus are discussed.     

Modified Glauber model for the total reaction cross-section of 12C + 12C collisions

Glauber's theory has been adopted to calculate the total heavy-ion reaction cross-sections at high energies. At relatively low energies, Glauber's total reaction cross-section has been modified in order to take into account the Coulomb field effect and is called modified Glauber model I. In addition to the Coulomb field effect, the nuclear effect has also been taken into account in the Glauber model and is called modified Glauber model II. An analytical expression for the transparency function for heavy-ion reactions, involving the nuclear densities of the colliding ions and the nucleon-nucleon cross- section, has been obtained within the framework of the modified Glauber models I and II. The transparency and the total reaction cross-sections of the ¹²C + ¹²C collisions are calculated at different bombarding energies. The obtained results are in good agreement with the experimental data and with previous theoretical calculations. Received: 26 January 2001 / Accepted: 15 October 2001     

Fusion, resonances and scattering in12C+12C reaction

The variation of fusion cross-section (σJ_fus) with energy in the¹²C+¹²C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σ_fus is taken as a part. The calculation of σ_fus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σ_fus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σ_fus data in the case of¹²C+¹²C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in¹²C+¹²C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of¹²C+¹²C reaction within the framework of optical potential model.     

One-nucleon transfer reactions in the12C+12C system at 344.5 MeV

Angular distributions of cross sections have been measured for single nucleon transfer reactions induced by 344.5 MeV¹²C ions on a¹²C target. DWBA analyses have been performed for transitions to discrete final states. Spectroscopic information has been derived and is compared with results of other studies.     

Total electron-scattering cross-section for molecular hydrogen at low energies by photoelectron spectroscopy

The relative total electron-scattering cross-section for molecular hydrogen has been measured in the energy region 0.02–1.14 eV. In general the Ramsauer technique is used for such a measurement, but in the present experiment the relative cross-sections have been measured by photoelectron spectroscopy. This is the first time that this technique has been put to such a use. The results in this energy region seem to match better the results of Ramsauer and Kollath than those of Golden et al.     

Parity nonconservation in the two-nucleon system at low energies

Parity violation (PV) effects inpp-scattering and thermalnp capture are reviewed. Current trends in the analysis of PV effects are outlined and new experimental results obtained at SIN are discussed.Presented at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Gammadecay of quasimolecular resonances in the12C+12C system

We have studied the heavy-ion radiative capture reaction¹²C(¹²C,γ)²⁴Mg forE _cm =4.7–6.0 MeV. Transitions to the ground-, first and unresolved second and third excited states in the final nucleus²⁴Mg have been observed with cross sections as low as 1 nb/sr. Forγ ₁ two strong resonance-like structures at 4.9 and 5.0 MeV were found correlated in energy with established 2⁺ resonances. Statistical model calculations cannot account for the observed yield. The branching ratioΓ _γ /Γ associated with theγ ₁ decay channel of the 5 MeV resonance was estimated to be 1.1·10^?5 yielding aγ-ray strength of 0.8 eV. The experimental result is in agreement with calculations based on the generator coordinate method where broad barrier resonances are viewed as short lived states of quasimolecular nature.     

Elastic and inelastic scattering of 12C ions at intermediate energies

Elastic and inelastic scattering of ¹²C ions on ¹²C and ²⁰⁸Pb targets have been measured at the incident energies per nucleon E / A = 120 MeV/u and E / A = 200 MeV/u. Optical-model analysis is reported and nuclear surface transparency effects are discussed, together with the nuclear potential-energy dependence. The transparency region extends down to a radial internuclear distance of about 3 fm for the ¹²C-¹²C system and 8 fm for the ¹²C-²⁰⁸Pb system. A decrease of the imaginary potential with increasing incident energy is deduced for the two systems. Anomalous collapse of the real potential in the surface region is observed for ¹²C-²⁰⁸Pb system at 200 MeV/u. DWBA analysis of data on the 2⁺, 4.4 MeV state of ¹²C is reported and trends for the energy dependance of mean-field excitations are deduced.     

Fusion cross section for 13C + 13C at low energies

The energy dependence of the fusion cross section has been measured over the range E_c.m. = 3.05–6.88 MeV by detecting the γ-rays from residual nuclei in a 4π geometry. Analyzing the 1.37 MeV photopeak, originating from ${}^{24}\text{Mg}\text{1.37}\text{MeV}\text{→}\text{g.s. transition}$, the cross sections for ²⁴Mg+2n channel were also deduced. The measured fusion cross sections have been compared with those for ¹²C + ¹²C and ¹²C + ¹³C systems and found to be significantly different. For ¹³C+¹³C the fusion cross sections agree with the standard optical-model prediction down to the lowest measured energies, while for ¹²C + ¹²C and ¹²C + ¹³C they are, at the lowest energies, too low. It is suggested that the unpaired valence nucleons facilitate fusion at energies well below the Coulomb barrier.